Worm and Worm Wheel:

Figure illustrates a worm and worm wheel. It consists of a worm which can be single start, double start or of higher starts. It gears with a toothed wheel which is called worm wheel. A wheel 'A' is associated to the shaft of worm over which a string or rope passes. The effort is applied at the free end of this string. The load is suspended through rope on the drum linked to the worm wheel as illustrated in the Figure

Consider W be the load lifted, P be the effort applied, R be the radius of wheel, r be the radius of load drum, T be the number of threads on work wheel, and n be the start of the worm.

For one rotation of the effort wheel,

Distance moved by the effort 'P' = 2 πR.

Distance moved by the load 'W' = 2 π r × (n/T)

Velocity ratio, V R = 2 π R/(2 π r ×   (n/T))    = RT/rn

Mechanical advantage,  M A = W /P

∴ Efficiency η = MA/ VR